Preheat oven to 425 degrees F(220 degrees C). Separate sliced onion into single rings.
In a medium sauce pan saute onions in butter until soft, approximately 20 minutes. Stir in flour and gradually add broth and water. Bring to a boil and simmer for 20 minutes.
Meanwhile, toast French bread slices.
Place toasted bread into soup bowls.
Pour soup mixture over bread and sprinkle with Parmesan and Swiss cheese.